We have developed a wideband phase-locked loop (PLL) circuit with real-time phase correction for high-speed and accurate force measurements by frequency modulation atomic force microscopy (FM-AFM) in liquid. A high-speed operation of FM-AFM requires the use of a high frequency cantilever which, however, increases frequency-dependent phase delay caused by the signal delay within the cantilever excitation loop. Such phase delay leads to an error in the force measurements by FM-AFM especially with a low Q factor. Here, we present a method to compensate this phase delay in real time. Combined with a wideband PLL using a subtraction-based phase comparator, the method allows to perform an accurate and high-speed force measurement by FM-AFM. We demonstrate the improved performance by applying the developed PLL to three-dimensional force measurements at a mica/water interface.